Lifting for manifold-valued maps of bounded variation

摘要

Let N be a smooth, compact, connected Riemannian manifold without boundary. Let E -> N be the Riemannian universal covering of N. For any bounded, smooth domain Omega subset of R-d and any u is an element of BV(Omega, N), we show that u has a lifting v is an element of BV(Omega, E). Our result proves a conjecture by Bethuel and Chiron. (C) 2019 Elsevier Inc. All rights reserved.